Individuals in the health care or food service industry regularly don disposable gloves in order to prevent the transmission of bacteria or other contaminants to themselves and to others. In certain cases, the disposable gloves are contained within, and dispensed from, a cardboard box. When donning a pair of gloves dispensed in this manner, a user typically grasps a glove and pulls the glove from the box using an uncovered hand. Once removed from the box, the user places the glove onto one of his uncovered hands. The user can then use his now covered hand to grasp and remove a second glove from the box and then place the second glove upon his ungloved hand.